quadrilateral_witherden_rule

quadrilateral_witherden_rule, a MATLAB code which returns a Witherden quadrature rule, with exactness up to total degree 21, over the interior of a quadrilateral.

The unit quadrilateral has vertices (0,0), (1,0), (1,1), (0,1).

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

quadrilateral_witherden_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

quadrilateral_witherden_rule_test

f90_rule, a Fortran90 code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).

Reference:

1. Freddie Witherden, Peter Vincent,
   On the identification of symmetric quadrature rules for finite element methods,
   Computers and Mathematics with Applications,
   Volume 69, pages 1232-1241, 2015.

Source Code:

• quadrilateral_unit_area.m, computes the area of a unit quadrilateral.
• rule_order.m, returns the number of quadrature points used in a rule of given degree.
• rule01.m, returns the rule of degree 1.
• rule03.m, returns the rule of degree 3.
• rule05.m, returns the rule of degree 5.
• rule07.m, returns the rule of degree 7.
• rule09.m, returns the rule of degree 9.
• rule11.m, returns the rule of degree 11.
• rule13.m, returns the rule of degree 13.
• rule15.m, returns the rule of degree 15.
• rule17.m, returns the rule of degree 17.
• rule19.m, returns the rule of degree 19.

• quadrilateral_witherden_rule_to_matlab.m, a MATLAB script which reads a data file describing one of the rules and writes a MATLAB function to return points and weights.